ID Number And Digit Arrangement (Posted on 2008-08-19)

Each of the ID numbers issued to Mr.Cooper and Mr. Duncan is of the form ABCDEFGHIJ, with each of the letters representing a different digit from 0 to 9 inclusively, such that:

(i) BCD is divisible by 2.

(ii) CDE is divisible by 3.

(iii) DEF is divisible by 5.

(iv) EFG is divisible by 7.

(v) FGH is divisible by 11.

(vi) GHI is divisible by 13.

(vii) HIJ is divisible by 17.

Determine the ID numbers issued to each of the gentlemen, given that the ID number of Mr. Cooper is greater than that of Mr. Duncan.

Note: A is not 0, and C is greater than D.

*** While a solution may be trivial with the aid of a computer program, show how to derive it without one.

There was a typographical anomaly in the note inclusive of the problem text, and the said note should read as:

"Note: A is not 0, A is greater than B, and C is greater than D."

Then, the solution in conformity with all the conditions would yield:

Mr. Cooper's ID Number = 4160357289

Mr. Duncan's ID Number = 4130952867

However, the problem text as posited, indeed admits of a multiplicity of solutions as has been rightly pointed out in the various comments.

Jyqm gives an analytic methodology in this location, and it may be observed that the said method would
give an unique solution, with the restriction A > B.

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